Boltzmann Sampler Line (PTSD / BNEM / DiKL)

Hernández-Lobato group's molecular generative-sampler thrust: the Progressive Tempering Sampler with Diffusion (PTSD, ICML 2025, joint with Aalto) combines parallel-tempering MCMC with diffusion training and beats prior diffusion samplers on target-evaluation efficiency for multimodal/Boltzmann targets, alongside the BNEM (TMLR 2025) and DiKL (AISTATS 2025) energy-/diffusion-based samplers for equilibrium molecular distributions. The same group unified score-based diffusion for PDE forecasting and data assimilation (NeurIPS 2024, cambridge-mlg/pdediff).